High performance equalizer having reduced complexity

ABSTRACT

An apparatus and method for implementing an equalizer which combines the benefits of a decision feedback equalizer (DFE) with a maximum-a-posterori (MAP) equalizer (or a maximum likelihood sequence estimator, MLSE) to provide an equalization device with significantly lower complexity than a full-state MAP device, but which still provides improved performance over a conventional DFE. The equalizer architecture includes two DFE-like structures, followed by a MAP equalizer. The first DFE forms tentative symbol decisions. The second DFE is used thereafter to truncate the channel response to a desired memory of L 1  symbols, which is less than the total delay spread of L symbols of the channel. The MAP equalizer operates over a channel with memory of L 1  symbols (where L 1 &lt;=L), and therefore the overall complexity of the equalizer is significantly reduced.

RELATED APPLICATIONS

[0001] This application claims priority of the following—U.S.Provisional patent application having Serial No. 60/265,740 (AttorneyRef. No. 13153US01), entitled “A Decision Feedback Equalizer for Minimumand Maximum Phase Channels,” filed Feb. 1, 2001; U.S. Provisional patentapplication having Serial No. 60/265,736 entitled “Method For ChannelEqualization For TDMA Cellular Communication Systems,” filed Feb. 1,2001; and U.S. Provisional patent application having Serial No.60/279,907, entitled “A Novel Approach to the Equalization of EDGESignals,” filed Mar. 29, 2001; all of which are hereby incorporated byreference in their entirety.

[0002] The application is also related to U.S. patent application havingSer. No. ______, entitled “Decision Feedback Equalizer for Minimum andMaximum Phase Channels,” filed ______, and hereby incorporated byreference.

FIELD OF THE INVENTION

[0003] The present invention provides an improved method and apparatusfor channel equalization in communication systems, wherein theadvantages of a decision feedback equalizer (DFE) are combined withthose of a non-linear equalizer, including a maximum-a-posteriori (MAP)or maximum-likelihood sequence estimator (MLSE) equalizer.

BACKGROUND OF THE INVENTION

[0004] This invention addresses the receiver design for digitalcommunication systems employing high-order modulation schemes andoperating in highly temporally dispersive channels. As an example, thisinvention has been applied to the EDGE standard (“Digital CellularCommunication System (Phase 2+) (GSM 05.01-GSM 05.05 version 8.4.0Release 1999)”). The EDGE standard is built on the existing GSMstandard, using the same time-division multiple access (TDMA) framestructure. EDGE uses 8-PSK (Phase-shift keying) modulation, which is ahigh-order modulation that provides for high-data-rate services. In8-PSK modulation, three information bits are conveyed per symbol bymodulating the carrier by one of eight possible phases.

[0005] A wireless channel is often temporally dispersive. In otherwords, after a signal is transmitted, a system will receive multiplecopies of that signal with different channel gains at various points intime. This time dispersion in the channel causes inter-symbolinterference (ISI) which degrades the performance of the system. FIG. 1shows a prior art example of a multipath channel profile. The mainsignal cursor 102 is followed in time by post-cursors 104, 106, 108, and110.

[0006] To combat the effects of ISI at the receiver, many differenttypes of equalization techniques can be used. One popular equalizationtechnique uses a Decision Feedback Equalizer (DFE). The DFE cancels theextraneous multipath components to eliminate the deleterious effects ofISI. A DFE is relatively simple to implement and performs well undercertain known circumstances. The performance of the DFE depends heavilyon the characteristics of the channel. A DFE typically performs wellover a minimum-phase channel, where the channel response has littleenergy in its pre-cursors, and its post-cursor energy decays with time.A DFE typically consists of a feed-forward filter (FFF) and a feedbackfilter (FBF). The FFF is used to help transform the channel into such aminimum-phase channel. Methods for computing the coefficients of the FFFand FBF (based upon channel estimates) are well known. See, e.g., N.Al-Dhahir and J. M. Cioffi, “Fast Computation of Channel-Estimate BasedEqualizers in Packet Data Transmission,” IEEE Trans. Signal Processing,vol. 43, pp. 2462-2473, November 1995, the contents of which areincorporated herein by reference.

[0007] Certain advantages of a DFE include good performance withrelatively low complexity. Certain disadvantages include, but are notlimited to: (1) Error propagation—i.e., once an error is made, thaterror is fed back and propagated into future symbol decisions. (2)Sub-optimum performance—i.e., instead of capturing multipath energy inthe channel, the DFE instead cancels out this energy. (3) Hard decisionoutput—i.e., a DFE makes a decision on the transmitted symbol withoutproviding any information associated with the reliability of thatdecision.

[0008] Other more complex equalization techniques utilize the multipathenergy from the received signal, rather than trying to cancel theenergy. Such equalizers include, but are not limited to, MLSE (MaximumLikelihood Sequence Estimation) and MAP (Maximum-A-Posterori)Estimation. These non-linear equalization techniques make adetermination as to the most likely transmitted symbols, based upon allof the available information to the receiver. The MLSE is the optimumsequence estimator over a finite channel response. The complexity of theMLSE equalizer grows exponentially with the channel response duration,and the equalizer produces hard symbol decisions. The MAP equalizeroperates in a similar fashion to the MLSE equalizer but provides softsymbol decisions. The primary disadvantage of the MAP equalizer iscomplexity. Hence, while these example equalizers are better at handlingproblematic signals, their implementations can prove to be very complexand expensive for systems using high-order modulation, such as the EDGEsystem. See G. David Forney. Jr., “Maximum-Likelihood SequenceEstimation of Digital Sequences in the Presence of IntersymbolInterference,” IEEE Trans. Inform. Theory, vol. 18, pp. 363-377, May1972; J. G. Proakis, “Digital Communications,” (3^(rd) edition) NewYork; McGraw-Hill, 1995. The contents of both the foregoing referencesare incorporated herein by reference.

[0009] The complexity of the MLSE and MAP equalizers, implemented usingthe known Viterbi algorithm (or the like), is exponentially proportionalto the memory of the channel. In particular, the number of statesrequired in the MLSE or MAP equalizer is given by M^(L), where M is thesize of the symbol alphabet and L is the memory of the channel insymbols. Moreover, the use of 8PSK modulation in the EDGE system makesthe complexity of the MLSE and MAP equalizers very large for channelswith moderate delay spreads. Note that different channel models existfor different types of terrain and are used to quantify receiversensitivity in the GSM standard. For example, the Hilly Terrain (HT)channel model has a profile that spans more than five symbols and wouldtherefore require an MLSE or MAP equalizer with 32,768 states to achieveacceptable performance.

[0010] Techniques to reduce the number of states of the MLSE have beenproposed. See, e.g., Alexandra Duel-Hallen and Chris Heegard, “Delayeddecision-feedback sequence estimation,” IEEE Transactions onCommunications, vol. 37, no. 5, p. 428-436, May 1989; M. Vedat Eybogluand Shahid U. Qureshi, “Reduced-state sequence estimation with setpartitioning and decision feedback,” IEEE Transactions onCommunications, vol. 36, no. 1, pp. 13-20, January 1988. Under thesetechniques, a subset of the full state space is chosen as the statespace, and a DFE is implemented on every state of the trellis (i.e., asshown in a state space diagram). However, the complexity of computingthe path metric values in these algorithms is still very large forchannels with a large delay spread.

[0011] Accordingly, what is needed in the field of the art is anequalizer device that provides for a simpler implementation, such as aDFE, but which provides the improved performance characteristics of amore complex equalizer, such as an MLSE or MAP. The equalizer should begenerally applicable to all digital communication systems but provideparticular advantage to coded systems using higher-order modulationschemes.

SUMMARY OF THE INVENTION

[0012] The present invention describes an equalizer which combines thebenefits of a decision feedback equalizer (DFE) with amaximum-a-posterori (MAP) equalizer (or a maximum likelihood sequenceestimator, MLSE) to provide an equalization device with lower complexitythan a full-state MAP or MLSE device, but which still provides improvedperformance over a pure DFE solution.

[0013] In the present invention, the equalizer architecture includes twoDFE-like structures, followed by a MAP equalizer. The channel responseis estimated and used to derive the coefficients of the feed-forward andfeedback filters. The coefficients of the feedback filter of the secondDFE are a subset of the coefficients of the first feedback filter.

[0014] The first DFE acts like a conventional DFE and forms tentativesymbol decisions. The second DFE is used thereafter to eliminate, orsubtract, the impact of certain post-cursors that exist past a certainmemory, L₁, (where L₁<=L) of the channel, by using the tentativedecisions formed by the first DFE. The effective channel response seenby the MAP equalizer is therefore constrained to a memory L₁, andtherefore the overall complexity of the equalizer is significantlyreduced. When the value of L₁ is zero, the proposed equalizerdegenerates to a conventional DFE. When the value of L₁=L, the proposedequalizer is a full state MAP equalizer. Therefore performance versuscomplexity trade-offs between a simple DFE and a full-state MAPequalizer can be made.

[0015] An MLSE equalizer might also be used in place of the MAPequalizer in the described configuration, if further complexityreduction is desired. However, usage of the MLSE will come at theexpense of receiver sensitivity.

[0016] Accordingly, one aspect of the present invention provides for areduced-state complexity equalizer apparatus for use with communicationsystems requiring equalization of a received incoming signal subject tointersymbol interference (ISI), the apparatus comprising: a firstdecision feedback equalizer device which utilizes coefficients derivedfrom the estimated channel response and forms tentative symboldecisions; at least a second decision feedback equalizer device whichutilizes coefficients derived from the estimated channel response andthe tentative symbol decisions from the first decision feedbackequalizer to truncate the channel response to a desired channel memory;at least one non-linear equalizer device for providing equalization ofthe channel response over the desired memory, whereby the overallcomplexity of the equalizer is reduced by reducing the effective delayspread of the channel.

[0017] Still another aspect of the present invention provides for amethod for reducing the complexity of an equalizer for use with acommunication system requiring equalization of a received incomingsignal subject to intersymbol interference (ISI), the method comprisingthe steps of: deriving feedback and feed-forward coefficients for theassociated feedback and feed-forward filters of a first and at least onesubsequent decision feedback equalizer from the estimated channelresponse; utilizing the first decision feedback equalizer to formtentative decisions regarding certain symbols; utilizing at least onesubsequent decision feedback equalizer to truncate the channel responseto a desired memory; utilizing at least one non-linear equalizer forproviding equalization of the channel response over the desired memory,whereby the overall complexity of the equalizer is reduced by reducingthe effective delay spread of the channel.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Certain aspects and advantages of the present invention will beapparent upon reference to the accompanying description when taken inconjunction with the following drawings, which are exemplary, wherein:

[0019]FIG. 1 is a prior art representation of typical multipath channelwith a time-decaying channel response.

[0020]FIG. 2 is a prior art diagram of an EDGE burst structure.

[0021]FIG. 3 is a prior art block diagram of representative transmitter,channel, and receiver.

[0022]FIG. 4 is a prior art block diagram of representative transmitterelements.

[0023]FIG. 5 is a prior art diagram of the encoding rule for an 8PSKmodulator.

[0024]FIG. 6 is a prior art diagram of the transmitted constellation foran 8PSK signal corresponding to FIG. 5.

[0025]FIG. 7 is a block diagram of representative EDGE receiverelements, wherein the channel estimation might incorporate certainaspects of the present invention.

[0026]FIG. 8 is a prior art diagram of the auto-correlation of TrainingSequences.

[0027]FIG. 9 is a prior art block diagram of representative DFEelements, with an associated channel response after the feed-forwardfilter.

[0028]FIG. 10 is a block diagram, according to one aspect of the presentinvention, of certain representative elements of an equalizer whichcombines a DFE with a MAP equalizer.

[0029]FIG. 11 is a block diagram, according to one aspect of the presentinvention, of a representative channel response showing the resultingelements of the truncated channel.

[0030]FIG. 12 is a block diagram, according to one aspect of the presentinvention, of certain representative elements of the present equalizerwhich combines a DFE with a MAP equalizer, and then also employssubsequent DFE/MAP equalizers, as needed.

[0031]FIG. 13 is a flowchart, according to one aspect of the presentinvention, of certain representative steps that can be used to implementthe present method of equalization.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0032] The present invention is described below in terms of certainpreferred embodiments, and representative applications. The apparatusand processing methods are applicable to any wireless or wirelinecommunication system where an equalizer is used to eliminate the ISIeffects of the channel.

[0033] A representative application of the invention is the EDGE system,and a preferred embodiment is described below. Since radio spectrum is alimited resource, shared by all users, a method must be devised todivide up the bandwidth among as many users as possible. The GSM/EDGEsystem uses a combination of Time- and Frequency-Division MultipleAccess (TDMA/FDMA). The FDMA part involves the division by the frequencyof the (maximum) 25 MHz bandwidth into 124 carrier frequencies spaced200 kHz apart. One or more carrier frequencies is assigned to each basestation. Each of these carrier frequencies is then divided in time,using a TDMA scheme. The fundamental unit of time in this TDMA scheme iscalled a burst period, and it lasts for 15/26 ms (or approximately 0.577ms). Eight burst periods are grouped into a TDMA frame (120/26 ms, orapproximately 4.615 ms) which forms the basic unit for the definition oflogical channels. One physical channel is one burst period per TDMAframe.

[0034] Many EDGE physical layer parameters are identical (or similar) tothose of GSM. The carrier spacing is 200 kHz, and GSM's TDMA framestructure is unchanged. FIG. 2 shows a representative diagram 200 of anEDGE burst structure. One frame 202 is shown to include eight timeslots. Each representative time slot 203 is shown to include a trainingsequence 204 of 26 symbols in the middle, three tail symbols 206, 208 ateither end, and 8.25 guard symbols 210 at one end. Each burst carriestwo sequences of 58 data symbols. The data sequences 212 and 214 areshown on either side of the training sequence 204.

[0035]FIG. 3 next shows a prior art block diagram 300 of a communicationsystem that consists of a transmitter 304, a channel 310, and a receiver320. The signal s(t) 302 represents a sequence of information that isgoing to be transmitted over a channel. The transmitted signalencounters a channel 310 (which includes multiplicative, dispersivecomponent 312 and additive white Gaussian noise component 314). Thereceiver 320 attempts to recover the original signal s(t) as receivedinformation bits 322.

[0036] A more specific block diagram of the transmitter portion 400 isshown in FIG. 4. In particular this diagram is described in terms of GSMand EDGE applications. The user data is first formatted into a frame viablock 402. Thereafter the data is convolutionally encoded and puncturedas shown in block 404. The signal is passed to an interleaver 406 thatscrambles the coded bits and distributes them across four bursts, shownas the burst builder block 408. The GMSK or 8PSK modulator is shownreceiving the subsequent signal in block 410.

[0037] For 8PSK modulation, the modulating bits are mapped in groups ofthree to a single 8PSK symbol. The encoding rule is shown in FIG. 5,where (d_(3i), d_(3i+1), d_(3i+2)) are the output bits from theinterleaver. These output symbols are then continuously rotated by aphase shift of 3/8 radians per symbol (the symbol rate is approximately270.833 ksps). These rotating 8PSK symbols are then pulse-shaped, usinga filter with an impulse response corresponding to the main component ina Laurant decomposition of a GMSK signal. As seen in FIG. 6, thispartial response signaling (caused by the pulse-shaping filter) causesthe transmitted signal to have appreciable amounts of ISI.

[0038] The transmitted signal thereafter passes through a multipathfading channel h(t) and is corrupted by additive white Gaussian Noisen(t). Assuming that the span of the overall channel response is finite,the discrete-time equivalent model of the received signal can be writtenas $\begin{matrix}{{r_{n} = {{\sum\limits_{k = 0}^{L}\quad {d_{n - k}h_{k}}} + \eta_{\eta}}},} & (1)\end{matrix}$

[0039] where L is the span of the composite channel response (consistingof the cascade pulse-shaping filter, propagation channel and thereceiver front-end filter), dn is the nth transmitted data symbol, {h₀,h₁, . . . , h_(L)} are the complex coefficients of the channel response,and η_(η) is the complex, zero-mean, white Gaussian random variable.

[0040] A block diagram of a typical EDGE receiver 700 is shown in FIG.7. The received signal, after analog-to-digital conversion, is passedthrough a digital low-pass filter 702 (or matched filter) to enhance thesignal-to-noise ratio within the signal bandwidth of interest. Afeed-forward filter (FFF) 704 is used to try to convert the channel to aminimum-phase channel. The FFF coefficients are computed in block 708based on the channel estimates, which along with the sample timing arederived from the correlation of the received signal with a knowntraining sequence. The output from the FFF is passed to an equalizer706, which attempts to eliminate the ISI having the composite responsegiven by the transmitter pulse, the channel impulse response, and thereceiver filter. The equalizer might be a DFE, MLSE, or MAP. In block710, the output from the equalizer is then reassembled into a frame, anda deinterleaver is applied (if needed). This signal is then passed tothe channel decoder 712, if channel coding was applied at thetransmitter.

[0041] Timing recovery and channel estimation—the timing recovery andchannel estimation are performed with the aid of the training sequence204 (in FIG. 2). The training sequence has the property that the resultof correlating the middle 16 symbols with the entire training sequenceyields a correlation function with identically zero values for +/−5symbols around the peak 802, as shown in FIG. 8.

[0042] For timing recovery, the oversampled received signal iscorrelated with the stored training sequence. The optimal symbol timingis given by the index of the subsample with the largest correlationvalue. Once the optimal symbol timing is determined, the estimates ofthe channel response, i.e., {h₀, h₁, . . . , h_(L)} are given by awindow of L+1 symbol-spaced correlation values with the largest sum ofenergy. Since the auto-correlation values given by the training sequenceare approximately zero for up to +/−7 symbols around the peak 802, themaximum window size L may be as large as 7. Since the duration of theburst is 0.577 ms, the channel can be assumed to be stationary duringthe burst for most vehicle speeds of practical interest.

[0043] Certain well-known equalization techniques are next discussed,including DFE and MLSE/MAP devices, followed by certain representativeembodiments of the proposed new technique.

[0044] Decision Feedback Equalizer—FIG. 9 shows a representative priorart block diagram 900 of a DFE device, which might be used as theequalizer device above. A standard DFE consists of two filters, afeed-forward filter (FFF) 902 and a feedback filter (FBF) 904. The FFFis generally designed to act as a whitened matched filter to thereceived incoming signal, thus maximizing the signal to noise ratio,while keeping the statistical properties of the noise Gaussian with zeromean. A representative signal (with interference) which might existafter the FFF is shown as 903, with signal rays h₀, h₁, h₂, and h₃. TheFBF 904 is used to reconstruct post-cursor interference using decisionsmade on previously detected symbols. After filtering 904, thepost-cursor interference is subtracted from the output of FFF 902, and asymbol decision 908 is made on this output.

[0045] Accordingly, the input to the decision device, in discrete form,is as follows: $\begin{matrix}{{z_{n} = {{\sum\limits_{k = {- N_{f}}}^{0}\quad {f_{k}r_{n - k}}} - {\sum\limits_{k = 1}^{N_{b}}{{\hat{\quad d}}_{{n - k}\quad}b_{k}}}}},} & (2)\end{matrix}$

[0046] where ƒ_(k), k=−N_(ƒ), . . . , 0 are the coefficients of thefeed-forward filter, b_(k), k=1, . . . , N_(b) are the coefficients ofthe feedback filter, and d

_(n) denotes the decision made on the symbol d_(n). The number of thefeedback coefficients N_(b) may be different from the memory of theoverall channel response L. Hereafter, we will assume N_(b)=L. Thecoefficients of the FFF and the FBF for the DFE can be computed using avariety of computationally efficient methods. One such method entitled“Fast Computation of Channel-Estimate Based Equalizers in Packet DataTransmission” has already been incorporated by reference above.

[0047] Soft-decision decoding might also be applied to the outputs ofthe DFE. As shown in FIG. 7, the symbol decisions from the equalizer arede-interleaved and passed to the channel decoder. Since soft-decisiondecoding improves the performance, the hard symbol decisions output fromthe DFE are weighted with the appropriate channel gain before they arepassed to the decoder. Typically a hard-decision is made on the symbold_(n) which is then weighted by a soft-value s_(o), as given by thefollowing equation, to produce an appropriate weighting forsoft-decision decoding. $\begin{matrix}{s_{o} = {\sum\limits_{k = 0}^{L}\quad {h_{k}h_{k}^{*}}}} & (3)\end{matrix}$

[0048] Hence, the soft value is a function of the channel coefficients.Other examples include making the soft value proportional to the energygain of the channel.

[0049] MLSE/MAP. An MLSE is the optimum equalizer in the presence offinite ISI and white Gaussian noise. The equalizer consists of a matchedfilter followed by a Viterbi algorithm. The complexity of the equalizeris determined by the number of states of the Viterbi algorithm, M^(L),where M is the symbol alphabet size and L is the memory of the channel.For high order modulations, such as 8PSK and 16QAM, the complexity ofthe equalizer is very large, even for moderate values of L.

[0050] Similar to the MLSE, the MAP criterion may be applied, resultingin an equalizer that has the same order of the complexity as the MLSE,but is able to produce soft symbol outputs. The soft symbol valuesimprove the performance of the subsequent channel decoder for a codedsystem.

[0051] For the MLSE or the MAP equalizer, the feed-forward filter can beimplemented as a matched filter with coefficients ƒ_(−k)=

_(K), k=0, . . . , L. Although the noise samples after the matchedfilter are non-white, the optimal path metric can be computed using themethod described by Ungerboeck (see Gottfried Ungerboeck, “Adaptivemaximum-likelihood receiver for carrier-modulated data-transmissionsystem,” IEEE Transactions on Communications, vol. COM-22, No. 5, pp.624-636, May 1974). The path metric in the nth interval is given by:$\begin{matrix}{{{Re}\lbrack {\alpha_{n}^{*}( {y_{n} - {\sum\limits_{i = 1}^{L}\quad {s_{i}\alpha_{n - i}}}} )} \rbrack},} & (4)\end{matrix}$

[0052] where y_(n) is the output of the matched filter, α_(n) is thehypothetical input symbol and α_(n−i), i=1, . . . , L is given by thestate of the trellis, and s_(i) is given by the following convolution:$\begin{matrix}{s_{i} = {\sum\limits_{k = 0}^{L - i}\quad {h_{k}^{*}h_{k + i}}}} & (5)\end{matrix}$

[0053] For the MLSE, the hard symbol decisions output from the equalizerare weighed according to Equation (3) prior to being passed to thechannel decoder. The MLSE/MAP equalizers typically achieve betterperformance over a DFE. Nevertheless, they are significantly morecomplex to implement than the DFE for the same channel memory.

[0054] The proposed approach for equalizing 8PSK (or other suchhigh-order) modulation signals consists of a combination of a DFE with aMAP equalizer (DFE-MAP). A block diagram of an embodiment of the presentinvention 1000 is shown in FIG. 10. The equalizer architecture consistsof two DFE-like structures 1002 and 1004, followed by a MAP equalizer1006. A feed-forward filter is shown as 1008. The first DFE 1002 actslike a conventional DFE and forms tentative symbol decisions. Thecoefficients of the feed-forward filter 1008 and the first feedbackfilter 1010 are derived from the channel estimates, as in theconventional DFE case. The coefficients of the second feedback filter1014 are a subset of the coefficients of the first feedback filter 1010.The input to the decision process 1012 is thus given by the priorEquation (2).

[0055] Accordingly, a sample channel response 1050 is shown after thefeed-forward filter 1008, containing signal rays h₀ through h₄. Thefirst DFE structure 1002 serves to first provide feedback signalsthrough the first feedback filter 1010 as shown by the signal rays h₁through h₄ in 1052.

[0056] The purpose of the second feedback filter 1014 is to eliminatethe impact of post-cursors (e.g., h₃ and h₄, shown by 1054) beyond L₁symbols (e.g., set at h₂), and thereby truncating the channel responseto a desired memory of L₁ symbols. The filter does this by cancelingthese post-cursors using the tentative decisions d

_(k) formed by the first DFE.

[0057] This is achieved by breaking the received signal after thefeed-forward filter 1008 into two parts, as shown by Equation (4), andthereafter constraining the maximum number of states in the MAPequalizer to be M^(L1) states out of a maximum possible of M^(L) for thefull state space. $\begin{matrix}{{\sum\limits_{k = 0}^{L_{1}}\quad {d_{n - k}b_{k}}} + {\sum\limits_{k = {L_{1} + 1}}^{L}\quad {d_{n - k}b_{k}}} + \phi_{n}} & (4)\end{matrix}$

[0058] where φ is the noise sample at the symbol rate after passagethrough the whitened-matched filter.

[0059] A tentative estimate of the data sequence, {d

_(n)} is produced by the first DFE structure 1002 (using hard symbolsdecisions of the z_(n) output of Equation (2)), and together with thefeedback coefficients, {b_(k)}, is used to limit the duration of theintersymbol interference to L₁ symbols.

[0060] Thus the input to the MAP equalizer becomes: $\begin{matrix}{{{\sum\limits_{k = {- N_{f}}}^{0}\quad {f_{k}r_{n - k}}} - {\sum\limits_{k = {L_{1} + 1}}^{L}\quad {{\hat{d}}_{n - k}\quad b_{k}}}},} & (5)\end{matrix}$

[0061] where L₁<=L. Since the MAP equalizer now operates only on M^(L1)states, the overall complexity of the equalizer is significantlyreduced.

[0062] For instance, with a channel memory of L=5, and a modulationorder of 8 (as used by 8PSK), a conventional MAP equalizer would require8⁽⁵⁻¹⁾ states, or 4096 states. By using the present system, theeffective channel memory seen by the MAP would be reduced to 3 (seesignal 1356) and the equalizer would only require 8⁽³⁻¹⁾ states, or 64states. With substantially fewer states, the proposed equalizerconfiguration would be much more manageable and less complex toimplement.

[0063]FIG. 11 next shows a graphical representation 1100 of thisrepresentative channel response having elements h₀ through h₄. When thevalue of L₁ (1102) is zero, the proposed equalizer degenerates to aconventional DFE, and when the value of the L₁=L (1104), the proposedequalizer is a full-state MAP equalizer. By choosing the appropriatevalue of L₁, certain performance and complexity trade-offs between a DFEand a full-state MAP equalizer can be made.

[0064] While not expressly shown, it should also be noted that an MLSEequalizer can be used instead of the MAP equalizer in the presentinvention. The MLSE device will further reduce the complexity of theimplementation but at the expense of receiver sensitivity. The presentinvention is not intended to be limited to the specific embodimentsshown above. FIG. 12 shows a block diagram having substantially the samecomponents (similarly numbered) as FIG. 10. After the MAP equalizer1006, however, a subsequent feedback filter 1204 is shown. The resultsof this subsequent feedback filter 1204 are then subtracted from theoutput of the feed-forward filter 1008. This signal is then fed into asubsequent MAP equalizer 1208 to provide a result 1212 which provideseven better performance characteristics. Note that the arrows 1208 and1210 are meant to indicate that even more feedback filters and MAPequalizers might be added, if further processing is needed. Note thatthe addition of such subsequent filters will increase the complexity ofimplementation, but (again) may provide for increased performance up tocertain limits, wherein additional filters will not be worth theirimplementation cost.

[0065]FIG. 13 next shows a representative flowchart of certain steps1300 that might be used to implement the present invention. In step1302, an estimate is taken of the channel, which is shown receiving anincoming signal 1301, as per the general approaches described above. Instep 1304, the feedback and feed-forward coefficients are derived forthe associated filters of the DFEs, based upon the estimate of thechannel response. In step 1306, the signal passes through a feed-forwardfilter whose coefficients have been determined above. In step 1308, afirst DFE (including at least a feedback filter and decision process) isutilized to form tentative symbol decisions. Step 1310 shows the secondDFE being used to cancel (or subtract) certain distant post-cursors. Thenumber of post-cursors to be cancelled depends upon the memory of thechannel response and the overall complexity desired (or a desired memoryof the channel) in the final implementation. The cancellation of suchpost-cursors serves to truncate the memory of the channel, whereby theoverall complexity of the equalizer is reduced by reducing the effectivedelay spread of the channel. Step 1312 next runs a MAP equalizer on thistruncated channel. Thereafter the resulting signal might be utilized(1314) as an equalized signal in any system that might require such anequalized signal.

[0066] Certain optional steps for implementation are shown in block1315. Step 1316 is shown canceling certain distant post-cursors (again,like 1310). This would be achieved by subsequent implementations of DFEcomponents (i.e., feedback filters in association with feed-forwardfilters, and linear equalizers) as implied by the arrows 1208 and 1210in FIG. 12. Block 1318 next shows the step of utilizing a subsequent MAPequalizer on the constrained signal. Decision block 1320 inquireswhether further processing is needed (or desired). If yes, then steps1316 and 1318 can be repeated as many times as might be needed withsubsequent equalizer implementations (again referring to elements 1208,1210 in FIG. 12). If no further processing is needed, then the flowproceeds to step 1314 where the resulting equalized signal is utilized.

[0067] Although the present invention has been particularly shown anddescribed above with reference to specific embodiment(s), it isanticipated that alterations and modifications thereof will no doubtbecome apparent to those skilled in the art. It is therefore intendedthat the following claims be interpreted as covering all suchalterations and modifications as fall within the true spirit and scopeof the invention.

1. A reduced-state complexity equalizer apparatus for use withcommunication systems requiring equalization of a received signalsubject to intersymbol interference (ISI), the apparatus comprising: afirst decision feedback equalizer device which utilizes coefficientsderived from the estimated channel response and forms tentative symboldecisions; at least a second-decision feedback equalizer device whichutilizes coefficients derived from the estimated channel response andthe tentative symbol decisions from the first decision feedbackequalizer to truncate the channel response to a desired channel memory;and at least one non-linear equalizer device for providing equalizationof the truncated channel response over the desired memory, whereby theoverall complexity of the equalizer is reduced by reducing the effectivedelay spread of the channel.
 2. The reduced-state complexity equalizerapparatus of claim 1, wherein the non-linear equalizer device includes amaximum-a-posterori (MAP) equalizer device.
 3. The reduced-statecomplexity equalizer apparatus of claim 1, wherein the non-linearequalizer device includes a maximum likelihood sequence estimator (MLSE)equalizer device.
 4. The reduced-state complexity equalizer apparatus ofclaim 1, wherein the first-decision feedback equalizer device includes afeed-forward filter and a feedback filter, and at least one seconddecision feedback equalizer device that includes a feedback filter. 5.The reduced-state complexity equalizer apparatus of claim 4, wherein thecoefficients of the feedback filter of the second-decision feedbackequalizer device is a subset of those of the feedback filter of thefirst-decision feedback equalizer device.
 6. The reduced-statecomplexity equalizer apparatus of claim 4, wherein post-cursorinterference is subtracted from the output of the feed-forward filter inthe first-decision feedback equalizer device and a hard symbol decisionis made on this output.
 7. The reduced-state complexity equalizerapparatus of claim 1, wherein the second-decision feedback equalizerdevice constructs partial post-cursor interference using the decisionfrom the output of the first decision feedback equalizer, and subtractsthe partial post-cursor interference from the output of the feed-forwardfilter.
 8. The reduced-state complexity equalizer apparatus of claim 1,wherein the output from the second-decision feedback equalizer isprovided as input to the non-linear equalizer device.
 9. A method forreducing the complexity of an equalizer for use with a communicationsystem requiring equalization of a received incoming signal subject tointersymbol interference (ISI), the method comprising the steps of:deriving feedback and feed-forward coefficients for the associatedfeedback and feed-forward filters of a first and at least one subsequentdecision feedback equalizer from the estimated channel response;utilizing the first decision feedback equalizer to form tentativedecisions regarding certain symbols; utilizing at least one subsequentdecision feedback equalizer to truncate the channel response to adesired memory; and utilizing at least one non-linear equalizer forproviding equalization of the truncated channel response over thedesired memory, whereby the overall complexity of the equalizer isreduced by reducing the effective delay spread of the channel.
 10. Themethod for reducing the complexity of an equalizer of claim 9, whereinthe non-linear equalizer includes a maximum-a-posterori (MAP) equalizerdevice.
 11. The method for reducing the complexity of an equalizer ofclaim 9, wherein the non-linear equalizer includes a maximum likelihoodsequence estimator (MLSE) equalizer.
 12. The method for reducing thecomplexity of an equalizer of claim 9, wherein the step of utilizing thefirst-decision feedback equalizer includes reconstructing post-cursorinterference using decisions made on previously detected symbols,subtracting the post-cursor interference from the output of thefeed-forward filter, and making a hard symbol decision on this output.13. The method for reducing the complexity of an equalizer of claim 9,wherein a further step of utilizing the second-decision feedbackequalizer includes: reconstructing partial post-cursor interferenceusing the hard symbol decision from the first-decision feedbackequalizer, subtracting the partial post-cursor interference from theoutput of the feed-forward filter, and saving the output.
 14. The methodfor reducing the complexity of an equalizer of claim 13, wherein afurther step of utilizing the non-linear equalizer includes: providingthe output from the second-decision feedback equalizer as the input tothe non-linear equalizer.